
Thickness and length of obstacles to account for different types of obstacles in real environment.

Error in robot pose to account for the possibility that it is not exactly at the centroid of a given cell.

Temperature of softmax.
It is important to normalize the ground truth likelihood to keep it bounded for a machine learning system to be able to learn. We use softmax with temperature \(\beta \)  defined as:
\(\sigma (p^{(0)}(z_t|x))_{n,m,\theta } = \frac{e^{\beta p^{(0)}(z_t|x)_{n,m,\theta }}}{\sum _{n,m,\theta } e^{\beta p^{(0)}(z_t|x)_{n,m,\theta }} }\) 
We vary the temperature parameter \(\beta \)  randomly within limits to make sure that it is not biased towards overly-uniform or overly-sharp likelihood outputs

Noise in the LiDAR scan: We train our network by adding Gaussian noise to every LiDAR scan point. Additionally, for every scan, we randomly set some of the incoming data points within the scan to have the value of \(+\infty \) .

There are errors in the actual map of the environment created using gmapping [1]}. This map is preprocessed and used as an input to the likelihood model and RL model for experiments on the real robot. Hence, it is important to ensure that some noise (more erosion and dilation of the map) is added to the map during training phase (on simulation) as well. However, note that the LiDAR readings will still come from the unperturbed map.

